On Thu, 12 Dec 2013 09:50:47 -0700, Jim Thompson wrote:

Another dawning while doodling at the beauty shop...

http://www.analog-innovations.com/SED/PieceWiseLinearThoughts_2013_12_12.pdf

... a way to join line segments easily to form PWL's, while
maintaining all derivatives at the joining points.

(Using my TANH version of greater than, less than... I'm working on
refining its coefficients to match segment slopes so there's no
"peaking" :-)

...Jim Thompson

How important is the continuity of higher order derivatives? Cubic
B-splines are continuous to the second order, becoming discontinuous
at the third, but are much easier/faster to calculate:
http://en.wikipedia.org/wiki/Spline_%28mathematics%29